//
//  riemansums1.java
//  riemansums1
//
//  Created by Chris Thiel on Sun Jan 26 2003.
//  Copyright (c) 2003. All rights reserved.
//  Free to use for education or by permission.
//  A simple Java applet that demonstrates the
//  notion of Riemann sums.
//

import java.awt.*;
import java.applet.Applet;
import java.io.*;
import java.awt.Graphics;
import java.awt.event.*;
import java.lang.Math;

public class riemansums1 extends Applet implements Runnable, AdjustmentListener {

int XMAX=400;
int YMAX=250;
int BOXMAX=150;
 //the next line creates the scrollbar used in this applet
    //with a max value of XMAX, and a min value of 1
    //takes integral from to to horiz scroller
    Scrollbar horiz0=new Scrollbar(Scrollbar.HORIZONTAL,1,20,-170,180);
    Scrollbar horiz1=new Scrollbar(Scrollbar.HORIZONTAL,1,20,-170,180);
  
    //the vertical scroll controls the number of rectangles
    //add 20 to maximum boxes to allow for the size of the arrows on either end
    Scrollbar vert=new Scrollbar(Scrollbar.VERTICAL,1,20,0,BOXMAX+20);
    Checkbox integrl=new Checkbox("Show actual area between axis and curve");
 final int quantum = 10;
 Image offScreenImage=null;
 Graphics offScreenGraphics = null;
 Dimension offScreenSize = null;
 Thread t;
 int h = 100;
 int h0 = 0;
 int v = 0;
 double boxArea = 0;
 double integral = 0;
 double a,b;
double delta;
 public void init() {
        Image img=null;
        h=100; h0=0;
        //the next sets the layout as a BorderLayout
        setLayout(new BorderLayout());

        //the next line adds horiz to South
        add("South",horiz0);
        add("North",horiz1);
       
        add("East",vert);
       // add("North",integrl);
        //the next line adds an adjusment listener to horiz so it can
        //have events processed when the scroller is moved
        horiz0.addAdjustmentListener(this);
        horiz1.addAdjustmentListener(this);
        vert.addAdjustmentListener(this);
        vert.setValue(BOXMAX);//Put vertical slider on bottom
        horiz0.setValue(0);
        horiz1.setValue(100);
	}
        
 //adjustmentValueChanged() is the method that handles AdjustmentEvents
    //which is when the value of a Scrollbar is changed
    public void adjustmentValueChanged(AdjustmentEvent e){
        //the next if statement checks to see if the AdjustmentEvent
        //came from horiz
        if(e.getAdjustable()==horiz0){
            //sets the text in num to the value of horiz
            h0 = horiz0.getValue();
       
            
        }
        if(e.getAdjustable()==horiz1){
            //sets the text in num to the value of horiz
     
            h = horiz1.getValue();
            
        }
        if(e.getAdjustable()==vert){
            //up is down in vertical location so subtract vertical sider location
            //from the max to put things in Cartsian order, where small is below
            v = BOXMAX-vert.getValue();
                    }
    }
public void run(){
		while (true) {
			
			update(getGraphics());
			try {
				Thread.sleep(quantum);
			}catch (InterruptedException e) {
				break;
			}
			
		
		}// of while
	} // of run
	
public void start() {
		t = new Thread(this);
		t.start();
	}
	
public void stop() {
		t.stop();
		t = null;
	}
public final void update (Graphics theG) {
		//implements no flickers
		Dimension dim = getSize();
		if ((offScreenImage==null)||(dim.width != offScreenSize.width)||(dim.height !=offScreenSize.height)) {
			offScreenImage = createImage(dim.width, dim.height);
			offScreenSize = dim;
			offScreenGraphics = offScreenImage.getGraphics();
		}
		//first clear old
		offScreenGraphics.clearRect(0,0,offScreenSize.width, offScreenSize.height);
		//now draw new
		paint(offScreenGraphics);
		//now put the offScreen Image on Screen!
		theG.drawImage(offScreenImage, 0,0,null);
	}// update
        
//convert graph coords to screen pixel location
 private int screenX (double x) {
	 return (int)(.5*XMAX+x*(XMAX/32));
	}

 private int screenY (double y) {
        return +1*(int)(.5*YMAX-y*(YMAX/22));
	}
        
//Find f(x) in terms of a screen coord
// ***** change this for a different function *****
private int f(double x){
    // the vertical screen coords go in the opposite direction as
    // the Cartisian Coordinate system, so make y values the
    // opposite sign.
    return screenY(0.04*x*x );
    }
//Find f(x) in terms of 10 time the graph system coords
// change this for a different function.  

private double f1(double x){
    return 0.04*x*x;
    }
private int d(double x){
// ***** change this for a different function *****
//  to be the deritative of f 
    return (int)(10*( 0.08*x));
}

private double dIntegral(double a, double b){
   return (b*b*b-a*a*a)/75.0; 
}

public void paint( Graphics g ) {
       
		g.setColor(new Color(0x108000)); //green background from (0,20) to (450,295)
		g.fillRect ( 0, 0, XMAX, YMAX);
		g.setColor(new Color(0x08602F)); //lines
                for(int i = -16; i< 17; i++) g.drawLine( screenX(i),0,screenX(i) ,YMAX); // horizontals
		for(int i = -11; i< 11; i++) g.drawLine( 0, screenY(i), XMAX,screenY(i) ); //virticals
		g.setColor(Color.black); 
		g.drawLine( 0, screenY(0), XMAX,screenY(0) ); // x-axis
		g.drawLine( screenX(0),0,screenX(0) ,YMAX);  // y=axis
               //draw boxes between curve and x-axis
                if (v!=0) {
                g.setColor(Color.yellow);
                delta=Math.abs((h-h0)/(10.0*v));
                    if (h < h0){
                        a=h/10.0;
                        b=h0/10.0;
                    }else{
                        a=h0/10.0;
                        b=h/10.0;
                    }
                boxArea=0;
                for(double x = a; x < b-(.5*delta); x=x+delta) {
                g.drawLine(screenX(x),f(x+delta),screenX(x+delta),f(x+delta) );
                g.drawLine(screenX(x),f(x+delta),screenX(x),screenY(0) );
                g.drawLine(screenX(x+delta),f(x+delta),screenX(x+delta),screenY(0) );
                boxArea=boxArea+delta*f1(x+delta);
                }
                }
                //draw boundry of interval
                g.setColor(Color.red);
                g.drawLine(screenX(h/10.0), screenY(0) ,screenX(h/10.0),f(h/10.0)); 
                g.setColor(Color.blue);
                g.drawLine(screenX(h0/10.0), screenY(0) ,screenX(h0/10.0),f(h0/10.0)); 
           
                //Draw the curve
                g.setColor(Color.white);
                for(double x = -17; x<17; x=x+.25) g.drawLine(screenX(x),f(x),screenX(x+.25),f(x+.25) );
            //Dislay info
                g.setColor(Color.red);
                g.drawString( "    b  = "+h/10.0, 220, 155 );
              
                g.setColor(Color.blue);
                g.drawString( "    a  = "+h0/10.0, 220, 170 );
                //g.drawString( "  f(x) = "+f1(h/10.0)/100.0, 220, 170 );
                if (v!=0) {
                g.setColor(Color.yellow);
                        
		g.drawString( "# of boxes = "+v, 220, 185 );
                g.drawString( "width of box = "+delta, 206, 200 );
                 g.drawString( "sum of box area = "+boxArea, 206, 215 );
                          
                }
                if(true){
                 g.setColor(Color.cyan);
                 g.drawString("Integral from a to b ="+dIntegral(a,b), 206, 230);
                }
            // Plot point (beginning interval )
            
                g.setColor(Color.blue);
                g.fillOval(screenX((h0/10.0))-2,f(h0/10.0)-2,5,5);
            //Plot point (x, f(x) )
                g.setColor(Color.red);
                g.fillOval(screenX(h/10.0)-2,f(h/10.0)-2,5,5);
                
            
                          //instructions
               g.setColor(Color.black);
                g.drawString("Change a with the bottom bar",20,YMAX-55);
                g.drawString("Change b with the top bar",20,YMAX-40);
               g.drawString("Change Æ with the vertical bar",20,YMAX-25);
	}

}